Solved example of express in terms of sine and cosine
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Combine all terms into a single fraction with $\cos\left(x\right)$ as common denominator
Divide fractions $\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$ with Keep, Change, Flip: $\frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}$
Multiply the single term $\cos\left(x\right)$ by each term of the polynomial $\left(1+\tan\left(x\right)\right)$
Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Multiplying the fraction by $\cos\left(x\right)$
Applying the trigonometric identity: $\tan\left(\theta\right)\cdot\cos\left(\theta\right)=\sin\left(\theta\right)$
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